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The features of a logically sound approach to a theory of statisticalreasoning are discussed. A particular approach that satisfies these criteria isreviewed. This is seen to involve selection of a model, model checking,elicitation of a prior, checking the prior for bias, checking for prior-dataconflict and estimation and hypothesis assessment inferences based on a measureof evidence. A long-standing anomalous example is resolved by this approach toinference and an application is made to a practical problem of considerableimportance which, among other novel aspects of the analysis, involves thedevelopment of a relevant elicitation algorithm.

Statistical Reasoning: Choosing and Checking the Ingredients, Inferences Based on a Measure of Statistical Evidence with Some Applications